CHAPTER 14

Chapter Overview

• Key Topics in Finance:

  • Present Value (PV)

  • Risk Aversion

  • Asset Valuation

  • Efficient Markets Hypothesis (EMH)

  • Market Irrationality

Present Value

• Definition:

  • The present value (PV) of a future sum is defined as the amount of money today that is necessary to produce a future amount of money (FV), considering prevailing interest rates.

• Future Value (FV):

  • The future value (FV) of a sum is the amount of money that a present sum of money (PV) will yield in the future based on the prevailing interest rates.

Example 1: Grandma's Gift

• Demarcus received $200 from his grandmother and wants to deposit it in the bank at 5% interest:

  • Present Value (PV): $200

  • Interest Rate (r): 0.05

  • Calculations:

  • In one year:
    $FV = 200 imes (1 + 0.05) = 210.00$

  • In two years:
    $FV = 200 imes (1 + 0.05)^2 = 220.50$

  • In three years:
    $FV = 200 imes (1 + 0.05)^3 = 231.53$

  • General formula for N years:
    $FV = PV imes (1 + r)^N$

Example 2: Saving for Grad School

• Amaia wants to determine how much to save to have $20,000 in 4 years with an 8% interest rate:

  • Use the formula for present value:

  • $PV = rac{FV}{(1 + r)^N}$

  • $PV = rac{20000}{(1 + 0.08)^4} = 14700.60$

Compounding and the Rule of 70

• Compounding:

  • Compounding refers to the process where the amount of money accrued earns additional interest on top of the interest already earned.

• Rule of 70:

  • To approximate the time it takes for an amount of money to double, divide 70 by the interest rate (in percentage).

Example 3: Compounding

• An investment of $1,000 in Microsoft stock:

  • Rate of Return = 8%:

  • $FV = 1000 imes (1 + 0.08)^{30} = 10063$

  • Doubling time: $70 / 8 = 8.75$ years

  • Rate of Return = 10%:

  • $FV = 1000 imes (1 + 0.10)^{30} = 17450$

  • Doubling time: $70 / 10 = 7$ years

  • Highlight: A 2% difference in interest leads to an over $7,000 difference in earnings.

Investment Decision: Power Plant

• Pacific Gas & Electric's power plant scenario:

  • Future Value: $800 million in 10 years

  • Present Value Calculations:

  • At 4% Interest: $PV = rac{800}{(1.04)^{10}} = 540.45$ million

    • Decision: Build the plant (cost < PV)

  • At 8% Interest: $PV = rac{800}{(1.08)^{10}} = 370.55$ million

    • Decision: Do not build (cost > PV)

Risk Aversion

• Definition of Risk Aversion:

  • Most people prefer to avoid uncertainty and thus dislike situations that may lead to loss.

• Utility:

  • A measure of well-being or satisfaction that is subjective.

• Diminishing Marginal Utility:

  • A principle that indicates losing $1,000 has a greater negative effect on utility than winning $1,000 positively affects it.

Markets for Insurance

• Function of Insurance:

  • Individuals pay a fee to an insurance company, which agrees to take on all or part of their risk. This pooling of risk assists risk-averse individuals.

Problems in Insurance Markets

• Adverse Selection:

  • High-risk individuals are more likely to purchase insurance.

  • Example: Individuals with chronic illnesses seeking health insurance.

• Moral Hazard:

  • Insured individuals may engage in riskier behavior.

  • Example: Individuals with good fire insurance may neglect safety precautions like changing smoke detector batteries.

Diversification of Firm-Specific Risk

• Standard Deviation:

  • A measure of volatility concerning variable returns.

• Diversification:

  • Risk reduction achieved by replacing a single risk with many smaller, unrelated risks.

  • Can eliminate firm-specific risk but not overall market risk.

Trade-Off Between Risk and Return

• Risk and return exhibit a trade-off:

  • Riskier assets generally yield higher average returns to compensate for added risks.

  • Historical Average Returns:

  • Stocks: 8%

  • Short-term government bonds: 3%

Example 4: Risk-Return Trade-Off

• Portfolio with:

  • Risky stocks (8% return, 20% standard deviation)

  • Safe asset (3% return, 0% standard deviation)

  • As stocks are added to the portfolio, the average return increases but so does the risk.

Asset Valuation

• When deciding on buying a company's stock, one must compare the share price against the value of the company:

  • Valuation Criteria:

  • Undervalued: Price < Value

  • Overvalued: Price > Value

  • Fairly valued: Price = Value

Example: Valuing AT&T Stock

• Analyzing a stock with:

  • Expected sell price: $30 in 3 years

  • Dividends: $1 at the end of each year for 3 years.

  • Present Value Calculation:

  • Year 1: $rac{1}{(1.1)} = 0.91$

  • Year 2: $rac{1}{(1.1)^2} = 0.83$

  • Year 3: $rac{1}{(1.1)^3} = 0.75$

  • Year 3 Sell Price: $rac{30}{(1.1)^3} = 22.54$

  • Total PV = $25.03

Efficient Markets Hypothesis (EMH)

• Definition of EMH:

  • This theory posits that asset prices reflect all publicly available information regarding value.

• Market Dynamics:

  • Stocks are actively followed by many money managers, with supply and demand determining price equilibrium.

• Informational Efficiency:

  • Stock prices adjust to reflect new information quickly and comprehensively, indicating a random walk behavior in prices.

Market Irrationality

• Psychological Influences:

  • Stock prices can also be driven by investor sentiments, termed as “animal spirits” (Keynes) or “irrational exuberance” (Greenspan)

• Speculative Bubbles:

  • Occurs when the price of an asset exceeds its fundamental value.

• Debate on Pricing:

  • Regular market movements challenge the rational pricing assumptions proposed by EMH.

Summary

• Key Takeaways:

  • Present value denotes a current amount necessary to generate a specified future amount, reflecting the time value of money.

  • Risk aversion motivates individuals to buy insurance and diversify their portfolios to mitigate uncertainty.

  • The value of an asset is determined by the present value of expected cash flows, with equity investors advised to favor diversified portfolios to optimize returns over time.

  • EMH asserts that stock prices reflect all available information, leading to debates on market psychology's influence against traditional rational market theories.